Coefficient estimates and subordination properties associated with certain classes of functions.
MSC 2010: 30C45Applications to starlike functions.
Let denote the open unit disk and f: → ℂ̅ be meromorphic and univalent in with a simple pole at p ∈ (0,1) and satisfying the standard normalization f(0) = f’(0)-1 = 0. Also, assume that f has the expansion , |z-p| < 1-p, and maps onto a domain whose complement with respect to ℂ̅ is a convex set (starlike set with respect to a point w₀ ∈ ℂ, w₀ ≠ 0 resp.). We call such functions concave (meromorphically starlike resp.) univalent functions and denote this class by resp.). We prove some coefficient...
The objective of this paper is to obtain sharp upper bound for the function for the second Hankel determinant , when it belongs to the class of functions whose derivative has a positive real part of order
The objective of this paper is to obtain sharp upper bound to the second Hankel functional associated with the root transform of normalized analytic function belonging to parabolic starlike and uniformly convex functions, defined on the open unit disc in the complex plane, using Toeplitz determinants.